We're dividing 555554 by 90 
We want to figure out the number of times 555554 can be divided by 90.

Moving on to step 1:
If we divide 5 by 90, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 90

Moving on to step 2:
55 divided by 90 is 0 with a remainder of 55.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Bring next digit (5) of the dividend behind the 55 and repeat the process: 555 / 90

Going ahead to step 3:
When dividing 555 by 90, we get 6 with a remainder of 15.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 540 from 555 and we're left with 15.
Bring next digit (5) of the dividend behind the 15 and repeat the process: 155 / 90

Moving on to step 4:
The number 90 fits into 155 1 times, leaving a remainder of 65.
Put 1 as the next digit of the answer. 
Result so far: 61.0
If we subtract 90 from 155, we get 65.
Take the next digit (5) from the dividend and append it to 65, then repeat: 655 / 90

Moving on to step 5:
90 can be fit into 655 7 times, resulting in a remainder of 25.
The next digit of our result is 7. 
Result so far: 617.0
If we subtract 630 from 655, we get 25.
Bring next digit (4) of the dividend behind the 25 and repeat the process: 254 / 90

Advancing to step 6:
90 can be fit into 254 2 times, resulting in a remainder of 74.
The number 2 becomes the next digit in our result. 
Result so far: 6172.0
If we take 180 away from 254, we end up with 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Let's proceed to step 7:
The number 90 fits into 740 8 times, leaving a remainder of 20.
The next digit of our result is 8. 
Result so far: 6172.8
The remainder is 20 after subtracting 720 from 740.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
The number 90 fits into 200 2 times, leaving a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 6172.82
Subtract 180 from 200 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 9:
The number 90 fits into 200 2 times, leaving a remainder of 20.
Write down 2 as next digit of the result. 
Result so far: 6172.822
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 6172.822, and the remainder is 0.002.